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  <div class="section" id="numpy-irr">
<h1>numpy.irr<a class="headerlink" href="#numpy-irr" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.irr">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">irr</code><span class="sig-paren">(</span><em class="sig-param">values</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/financial.py#L745-L829"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.irr" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Internal Rate of Return (IRR).</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 1.18: </span><a class="reference internal" href="#numpy.irr" title="numpy.irr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">irr</span></code></a> is deprecated; for details, see NEP 32 <a class="reference internal" href="#r709af50a60b2-1" id="id1">[1]</a>.
Use the corresponding function in the numpy-financial library,
<a class="reference external" href="https://pypi.org/project/numpy-financial">https://pypi.org/project/numpy-financial</a>.</p>
</div>
<p>This is the “average” periodically compounded rate of return
that gives a net present value of 0.0; for a more complete explanation,
see Notes below.</p>
<p><a class="reference external" href="https://docs.python.org/dev/library/decimal.html#decimal.Decimal" title="(in Python v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">decimal.Decimal</span></code></a> type is not supported.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>values</strong><span class="classifier">array_like, shape(N,)</span></dt><dd><p>Input cash flows per time period.  By convention, net “deposits”
are negative and net “withdrawals” are positive.  Thus, for
example, at least the first element of <em class="xref py py-obj">values</em>, which represents
the initial investment, will typically be negative.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">float</span></dt><dd><p>Internal Rate of Return for periodic input values.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The IRR is perhaps best understood through an example (illustrated
using np.irr in the Examples section below).  Suppose one invests 100
units and then makes the following withdrawals at regular (fixed)
intervals: 39, 59, 55, 20.  Assuming the ending value is 0, one’s 100
unit investment yields 173 units; however, due to the combination of
compounding and the periodic withdrawals, the “average” rate of return
is neither simply 0.73/4 nor (1.73)^0.25-1.  Rather, it is the solution
(for <img class="math" src="../../_images/math/79a3d439d28652c547386f39b555d90d3aaf102d.svg" alt="r"/>) of the equation:</p>
<div class="math">
<p><img src="../../_images/math/1ac05781fa44715441630253daee8891e22717b2.svg" alt="-100 + \frac{39}{1+r} + \frac{59}{(1+r)^2}
+ \frac{55}{(1+r)^3} + \frac{20}{(1+r)^4} = 0"/></p>
</div><p>In general, for <em class="xref py py-obj">values</em> <img class="math" src="../../_images/math/fafb6fc7385badc5a645cf8e265d3527362d28f6.svg" alt="= [v_0, v_1, ... v_M]"/>,
irr is the solution of the equation: <a class="reference internal" href="#r709af50a60b2-2" id="id2">[2]</a></p>
<div class="math">
<p><img src="../../_images/math/87f07f16060e4229d08f41accafc809b62a74c86.svg" alt="\sum_{t=0}^M{\frac{v_t}{(1+irr)^{t}}} = 0"/></p>
</div><p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r709af50a60b2-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>NumPy Enhancement Proposal (NEP) 32,
<a class="reference external" href="https://numpy.org/neps/nep-0032-remove-financial-functions.html">https://numpy.org/neps/nep-0032-remove-financial-functions.html</a></p>
</dd>
<dt class="label" id="r709af50a60b2-2"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
<dd><p>L. J. Gitman, “Principles of Managerial Finance, Brief,” 3rd ed.,
Addison-Wesley, 2003, pg. 348.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">irr</span><span class="p">([</span><span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">39</span><span class="p">,</span> <span class="mi">59</span><span class="p">,</span> <span class="mi">55</span><span class="p">,</span> <span class="mi">20</span><span class="p">]),</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">0.28095</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">irr</span><span class="p">([</span><span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">74</span><span class="p">]),</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">-0.0955</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">irr</span><span class="p">([</span><span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">7</span><span class="p">]),</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">-0.0833</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">irr</span><span class="p">([</span><span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">]),</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">0.06206</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">irr</span><span class="p">([</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mf">10.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">8</span><span class="p">,</span> <span class="mi">1</span><span class="p">]),</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">0.0886</span>
</pre></div>
</div>
</dd></dl>

</div>


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